Question

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 205 , 201 , 197 , . . . Find the 48th term.

Answer 1

Answer: 17

Explanation:

1. First we find out how to get from 1 term to the next:

205 - 201 = 4, 201 - 197 = 4, and the sequence is decreasing each time so -4, -4n

2. Next we determine the difference between the sequence, and the -4 times table

205 201 197

-4 -8 -12

205 - - 4 = 201, 201 - - 8 = 209, etc...

so the difference is positive 209 (+209)

3. Next, we use the nth term rule (-4n+209), and substitute 48 into n:

-4 x 48 + 209

-4 x 48 = -192, -192 + 209 = 17

4. So 17 is the 48th term.

Answer 2

Explanation:

To find the 48th term of the sequence, we need to determine the pattern or rule governing the sequence. From the given sequence, we can observe that each term is decreasing by 4 from the previous term. This means that the common difference between the terms is -4.

Using this information, we can write the general formula for the nth term of the sequence. The formula for the nth term of the sequence would be:

y = x + (n-1)d

where y is the nth term of the sequence, x is the first term, n is the position of the term we want to find, and d is the common difference.

Substituting the given values, we get:

x = 205

d = -4

Now we can plug in n = 48 and solve for the 48th term:

y = x + (n-1)d

y = 205 + (48-1)(-4)

y = 205 - 188

y = 17

Therefore, the 48th term of the sequence is 17.